Problem: Multiply the following complex numbers: $({-5+5i}) \cdot ({5-i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-5+5i}) \cdot ({5-i}) = $ $ ({-5} \cdot {5}) + ({-5} \cdot {-1}i) + ({5}i \cdot {5}) + ({5}i \cdot {-1}i) $ Then simplify the terms: $ (-25) + (5i) + (25i) + (-5 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -25 + (5 + 25)i - 5i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -25 + (5 + 25)i - (-5) $ The result is simplified: $ (-25 + 5) + (30i) = -20+30i $